78 citations · 188 across the 31 of their papers we have counts for
37 papers
Global minimality of the degree-one Ginzburg-Landau vortex solution in the unit ball in dimensions
Radu Ignat, Luc Nguyen
We consider the problem of minimizing the Ginzburg-Landau functional among -valued maps from the unit ball with vortex boundary condition $u(…
The Ginzburg-Landau system with general potential: maximum principle and gradient estimates
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We study critical points of the Ginzburg-Landau energy functional $$\mathcal{F}_\varepsilon[u] = \int_Ω\Big[ \frac{1}{2}|\nabla u|^2 + \frac{1}{2\varepsilon^2} W(1 - |u|^2)\Big]\,d…
Asymptotic minimality of one-dimensional transition profiles in Aviles-Giga type models: an approach via 1-currents
Radu Ignat, Roger Moser
For vector fields on a two-dimensional domain, we study the asymptotic behaviour of Modica-Mortola (or Allen-Cahn) type functionals under the assumption that the divergence converg…
The conformal limit for bimerons in easy-plane chiral magnets
Bin Deng, Radu Ignat, Xavier Lamy
We study minimizers of the energy functional \begin{align*} E_σ(\boldsymbol{m}) = \int_{\mathbb R^2} \bigg(\frac 12 |\nabla\boldsym…
A short proof of the regularity for the eikonal equation
Radu Ignat
We give a short and self-contained proof of the interior regularity of solutions to the eikonal equation in an open set $Ω\sub…
Renormalised energy between boundary vortices in thin-film micromagnetics with Dzyaloshinskii-Moriya interaction
Radu Ignat, François L'Official
We consider a three-dimensional micromagnetic model with Dzyaloshinskii-Moriya interaction in a thin-film regime for boundary vortices. In this regime, we prove a dimension reducti…